UNIVERSAL DRAFTING INSTRUMENT LS-2

L. S. SKRIPOV

(Presented by the scientific seminar of the Department of Descriptive Geometry and Graphics)

In 1949 the author of the present work designed the universal drafting instrument LS-1, whose purpose was to carry out, by mechanical means, the construction of:

1) perspective images from two orthogonal projections of an object;
2) self-shadows and cast shadows on the orthogonal projections of an object;
3) axonometric images of any kind from two orthogonal projections of an object;
4) and, finally, to use the instrument as an ordinary drafting device replacing a T-square and a set square.

The creation of such a mechanism was intended to simplify, accelerate, and reduce the cost of graphic work connected with the tasks listed above, and to concentrate them in a single instrument.

The author succeeded in creating one of the variants possible for mechanisms of this kind, for which an author’s certificate was issued (Gostekhnika of the USSR) under No. 90373 of 21/XI 1949, with priority from 28/III 1950.

Such mechanisms, of course, may be of various designs, differing in merits and shortcomings, and in order to obtain more perfect instruments further research work in this direction is needed.

In the present work the author proposes a somewhat different design of a universal drafting instrument, which performs the above-mentioned tasks and possesses better qualities than the preceding type. The author calls it the “Universal Drafting Instrument LS-2,” in contrast to the first “Universal Drafting Instrument LS-1.”

Theoretical substantiation of the drafting instrument as an instrument for constructing perspective

For greater clarity in the operation of the instrument it is necessary briefly to recall the theoretical substantiation of its design.

In Fig. 1 two arbitrary points \(1, 1'\) and \(2, 2'\) are shown in orthogonal projections. An arbitrarily located picture plane \(Q\), specified by the traces \(Q_H\) and \(Q_V\), is chosen. The pole of projection—the point \(P\)—is chosen. Projecting the points \(1\) and \(2\) taken onto the plane \(Q\), we obtain their central projections \(1_1, 1_1'\), and \(2_1, 2_1'\). For better consideration

of the obtained projections, the plane \(Q\) should be made to coincide with the frontal plane \(V\) by rotation about the trace \(Q_v\). For the mechanical construction of the central projections of points 1 and 2 on the superposed plane \(Q\), the author developed the design of the drawing instrument LS-1 (Universograph LS-1).

The projecting rays are replaced by two rods fixed at the points \(p\) and \(p'\) (the projections of the viewpoint—the pole). By rotating these rods, they can be set to any point of the drawing, and in our case to the points \(1, 1'\) or \(2, 2'\).

Fig. 1

Instead of the trace of the picture plane \(Q_H\), a ruler has been created, along which a carriage moves with free motion. Attached to the carriage is a ruler perpendicular to the trace \(Q_H\). Such a mechanism simplifies the construction of the perspective of any point, as can easily be seen from Fig. 1.

By rotation about the point \(p\), the lower rod is set on the horizontal projection of point 1, and the upper rod—on its frontal projection, \(1'\).

The carriage on the ruler \(Q_H\) is set at point 1; the vertical line drawn from point 1 will meet the rod at the point \(1'\)—the vertical projection of the perspective of point 1.

The ruler perpendicular to \(Q_H\) will intersect, at the point \(1_2\), the line \(T_2\), located in any free place of the drawing on the right and parallel to the bisector \(T_1\) of the angle \(\alpha\).

By drawing a vertical line from the point \(1_2\), and a horizontal line from the point \(1'\), the desired perspective of the point \(1'_2\) is found at their intersection on the superposed picture plane and transferred to the right to any free place of the drawing.

To simplify the constructions still further, the instrument is placed on a box with glass, on which a grid of vertical and horizontal lines has already been applied. Paper is laid on the glass and illuminated from below through the glass, which makes it possible not to draw vertical lines

Fig. 2

Visible figure labels include: View A, View B, View C, View D, View E, View F, View K, View Г.

Other visible designations and callouts are numeric part labels and geometric/reference marks: \(A\), \(B\), \(C\), \(C_1\), \(D\), \(D_1\), \(E\), \(K\), \(X\), \(X_1\), \(M\), \(H\), \(O\), \(a\), \(a'\), \(a''\), \(B_0\), \(B_2\), and part numbers \(1\)–\(24\).

and horizontal lines, but only to mark the required perspective of the point \(1\) \((1'_2)\).

In Fig. 1 the scheme of the mechanism is shown by thick lines.

Structural design of the LS-2 drafting instrument

The main part of the LS-2 instrument is a rectangular frame 1 (Fig. 2) made of round rods. The frame is mounted on four screws 2 with pointed ends for stability and for adjusting its height above the drawing.

Sleeves 3 can move along the rods of the frame and be secured with screws 4. The sleeves carry rod 5 with sleeves 6 that can be repositioned on it. Rod 5 and sleeves 6 can be set on the projections \(p\) and \(p'\) of the viewpoint and firmly fixed in this position by screws 7, which gives firm fixation of the points \(p\) and \(p'\) as centers of rotation of the projecting rods 8.

On the same frame, sleeves 14 can move and set rod 15 in the selected direction of the picture plane \(Q_H\). In this position rod 15 is secured by screws. The position of the rod may be chosen arbitrarily. Rod 15 replaces the guide ruler of the LS-1 univergraph, thus creating the necessary stability in this direction for the carriage. About the centers \(p\) and \(p'\), the projecting rays 8 can rotate and be set on the corresponding projections of given points, for example, the points \(a, a'\).

Fig. 3

Carriage 18 can move along rod 15; it is connected with sleeve 10 when the latter is moved, depending on the place where the lower rod 8 is installed. The projecting rods 8 move in a plane located lower than the plane in which rod 15 is located, and this design eliminates the possibility of some rods catching on others. Carriage 18 carries ruler 21, arranged at a right angle to rod 15 and so that its edge intersects in space with the continuation of the edge of ruler 24 on rod 8 at the point of the center of a transparent semicircle with degree divisions. The edge of ruler 21

intersected by the ruler \(T_2\), parallel to the line \(T_1\)—the bisector of the angle of inclination of rod 15 with the \(OX\) axis, at the point \(a_2\). The perspective of the point \(a'_2\) taken will be determined if, from the center of the half-disk of ruler 21, a vertical line is drawn until it meets ruler 24 on the upper rod 8 at the point \(a'_1\), and from this point a horizontal line is drawn until it meets the vertical line drawn from the point \(a_2\). In order to avoid drawing the auxiliary lines \(a_1a'_1\), \(a'_1a_2\), and \(a_2a'_2\) on the drawing and thus not clutter it with unnecessary lines, and to speed up the process of constructing the perspective of individual points, the entire instrument is mounted on box 25 (Fig. 3) with a glass cover 26, ruled in the form of a grid of horizontal and vertical lines. The drawing is placed on the glass and illuminated from below by electric lamps, thereby creating a shadow grid on the glass. Drawing the lines \(a_1a'_1\), \(a'_1a_2\), \(a_2a'_2\) is no longer required; only their mutual intersection at the point of the required perspective \(a'_2\) is marked. The installation of the entire instrument on box 25 is clear from Fig. 3, in which the designations of all elements of the instrument correspond to their designations in Fig. 2. An example of constructing the perspective of a cube is shown in Fig. 2 from its two orthogonal projections and the chosen viewpoint \(p, p'\). The projections of all vertices of the cube are found by the method described above and are then connected by straight lines. To check the correctness of the construction of the perspective lines by means of the instrument, one may also determine the vanishing point of the perspective lines \(p_2\).

Drafting Instrument LS-2 as an Instrument for Constructing Axonometric Projections

The proposed design may be used as an “axonograph,” as a mechanism that constructs axonometry with arbitrary distortion coefficients along the axes. The design of the axonograph was developed by the author in a separate work and published in the TEKhSO library under No. 939/21 in 1942. In the present work only the application of the LS-2 drafting instrument as an axonograph is shown. The frame of the instrument 1 (Fig. 4) is placed on a drawing with two projections of some object. On rod 5 of the instrument there remains only one coupling 6, at the point \(p\) of which both rods 8 are fastened on a single screw. Rods 8 can rotate about the point \(p\) and be set at any angles \(\varphi\) and \(\psi\) to the horizontal line of the drawing.

Along the rods there can slide two couplings each, with rulers 27 and 28, 30 and 31. Rulers 27 and 28, as well as 30 and 31, can move only jointly, since they are connected by rods 29 and 32, and can be positioned at different distances from one another as desired.

Rulers 27 and 28, 30 and 31 are set at definite angles \(\varphi_1\) and \(\varphi_2\), \(\psi_1\) and \(\psi_2\) relative to rods 8, depending on the desired type of axonometric representation. The angles \(\varphi\) and \(\psi\) also depend on the type of axonometry intended.

The construction of the couplings with the rulers fastened to them is shown in Fig. 2. Couplings 9 end below in disks 22 with degree divisions. Around the axes of these disks, the lower disks 23 can rotate, with rulers 24 fastened in them, and be set at the required angles \(\varphi_1\), \(\varphi_2\), \(\psi_1\), and \(\psi_2\) to the axes of rods 8 (Fig. 4).

To obtain the axonometry of an object, it is sufficient to set the edges of rulers 28 and 31 on the projections of some point, for example, \(a, a'\) (Fig. 4), and at the intersection of rulers 27 and 30 its axonometric image will be found in the form of the point \(a_1\).

The same procedure should be followed in finding the axonometric projections of other points of the object, which are then connected with one another...

…by lines. In Fig. 4 a dimetric image of a certain angle bracket with ribs is constructed.

Fig. 4

Below is a table of the angles for setting the rods and rulers for constructing certain axonometric projections.

Table

The magnitudes of the angles \(\varphi, \psi, \varphi_1, \varphi_2, \psi_1, \psi_2\) may be calculated theoretically for any type of axonometric projections of rectangular and oblique projection on the basis of the theory proposed by the author in his work Axonograph.

The LS-2 drafting instrument as an instrument for constructing shadows in orthogonal projections

The proposed design of the LS-2 drafting instrument can also be used for the mechanical construction of shadows on orthogonal drawings. For this purpose, on the frame of instrument 1 (Fig. 5) there remains rod 5 with sleeve 6, at point \(p\) of which rods 8 are fastened on a screw, inclined to the line \(OX\) at any arbitrary angles \(\varphi\) and \(\psi\).

Fig. 5

Rulers 27 and 30 are set at angles \(\varphi_1\) and \(\psi_1\) to rods 8 so that they must form angles of \(45^\circ\) with the axis \(OX\). The magnitudes of the angles \(\varphi_1\) and \(\psi_1\) can be calculated for the angles \(\varphi\) and \(\psi\), at which rods 8 are placed relative to the axis, from the expressions

\[ \varphi_1 = 180^\circ - \varphi - 45^\circ,\quad \psi_1 = 180^\circ - \psi - 45^\circ. \]

If the inclinations of the projections of the light rays to the axis \(OX\) are taken to be different from \(45^\circ\), then their values should be substituted instead of 45 in the above expressions for the angles \(\varphi_1\) and \(\psi_1\).

To find the shadows of points, it is sufficient to set the inner edges of rulers 27 and 30 on the corresponding projections of the points, for example, \(a\) and \(a'\), mark the points of intersection of one of the rulers with the axis \(OX\) (in the example in Fig. 5, ruler 27), and from the point of intersection with \(OX\) restore the per-

perpendicular to the axis \(OX\) until it meets the edge of the other ruler 30 at the point \(a'_1\), which will be the shadow of the point \(a\), \(a'\) on the vertical projection plane.

The LS-2 drafting instrument is mounted on the box shown in Fig. 5; the drawing is illuminated from below, and, if there is a grid on the glass, it is not necessary to draw auxiliary lines on the drawing, but only to mark the shadows of points on the projection planes.

The LS-2 drafting instrument as a drafting machine

The proposed design of the LS-2 drafting instrument makes it possible to use the instrument as an ordinary drafting machine, replacing the straightedge and the set square. The frame of the instrument 1 (Fig. 6) is placed on

Fig. 6

a sheet of paper; rod 5 is mounted on the frame and firmly secured by couplings 3. A coupling 6 is mounted on rod 5 closer to its lower end and is firmly secured. At point \(p\) of the coupling, both rods 8 are connected and are likewise firmly secured in the selected position at any angle relative to one another.

Rulers 27 and 30 can move freely along rods 8; the angles at which they are set, \(\varphi_1\) and \(\psi_1\), relative to rods 8 are chosen so that ruler 30 is horizontal, and ruler 27 is vertical and perpendicular to 30. Ruler 30 replaces the straightedge, and ruler 27 replaces the set square.

Thus, by moving rulers 30 and 27 along rods 8, one can construct any projections of an object.